In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. If the waiting time (in minutes) at each stop has a uniform distribution with A = 0 and B = 5, then it can be shown that the total waiting time Y has the pdf below. 25% osy<5 f(y) = 5 sys 10 0 y <0 or y> 10 (a) Sketch a graph of the pdf of Y. f(y) f(y) f(y) f(y) 0.20k 0.20 0.20 0.20k 0.15 0.15 0.15 0.15 ÍZKEZA. 0.10 0.10 0.10 0.10 0.05 0.05 0.05 0.05 y 2 4 6 O 8 10 2 4 8 O 6 10 8 O 2 4 6 10 2 4 6 8 10 (b) Verify that t [*^ Ry) dy = 1. 10 f(y) dy= 5 525 (c) What is the probability that total waiting time is at most 3 min? (d) What is the probability that total waiting time is at most 9 min? 25
In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. If the waiting time (in minutes) at each stop has a uniform distribution with A = 0 and B = 5, then it can be shown that the total waiting time Y has the pdf below. 25% osy<5 f(y) = 5 sys 10 0 y <0 or y> 10 (a) Sketch a graph of the pdf of Y. f(y) f(y) f(y) f(y) 0.20k 0.20 0.20 0.20k 0.15 0.15 0.15 0.15 ÍZKEZA. 0.10 0.10 0.10 0.10 0.05 0.05 0.05 0.05 y 2 4 6 O 8 10 2 4 8 O 6 10 8 O 2 4 6 10 2 4 6 8 10 (b) Verify that t [*^ Ry) dy = 1. 10 f(y) dy= 5 525 (c) What is the probability that total waiting time is at most 3 min? (d) What is the probability that total waiting time is at most 9 min? 25
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Solve part B through F
Transcribed Image Text:In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. If the waiting time (in minutes) at each stop has a uniform distribution with A = 0 and B = 5, then it can be shown that the total waiting time Y has the pdf
below.
0 ≤ y < 5
f(y) =
#
5 ≤ y ≤ 10
25
0
y <0 or y> 10
(a) Sketch a graph of the pdf of Y.
f(y)
f(y)
f(y)
f(y)
0.20
0.20
0.20
0.20k
0.15
0.15
0.15
0.15
IZUIZN
0.10
0.10
0.10
0.10
0.05
0.05
0.05
0.05
V
y
y
2
4
6
8
10
O
2
4
6
8
10
2
4
6
8
10
4
6
8
10
(b) Verify that
f(y) dy = 1.
+ [° F(x)
[Andy=[
10
5
= 1/2+
(c) What is the probability that total waiting time is at most 3 min?
(d) What is the probability that total waiting time is at most 9 min?
(e) What is the probability that total waiting time is between 3 and 9 min?
(f) What is the probability that total waiting time is either less than 4 min or more than 7 min?
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